Transmission filtering using machine learning

ABSTRACT

Systems and methods for transmission filtering are provided. A receiver includes an input coupled to a transmission line to receive distorted optical symbols. A distortion filter is coupled to the input to replace the distorted optical symbols with predicted symbols using a trained neural network. A decoder is coupled to the distortion filter to decode the predicted symbols.

RELATED APPLICATION INFORMATION

This application claims priority to US Provisional Application Number62/569,723, filed on Oct. 9, 2017, incorporated herein by referenceherein its entirety.

BACKGROUND Technical Field

The present invention relates to transmission filtering methods anddevices and more particularly, to symbol filter systems and methods thatemploy trained neural networks to compensate for filter narrowingeffects.

Description of the Related Art

When optical signals propagate over an optical transmission system,inter-symbol interference (ISI) may occur in which one symbol interfereswith other symbols. Thus, ISI introduces additional noise into theoptical signals and makes the transmission systems less reliable. A maintype of ISI is filter narrowing, which happens when narrower filtersthan the data rate along an optical path are used to increase spectralefficiency. The cascading filtering effect heavily affects the shape ofthe transmitted signal, and the received signal at the receiver ishighly distorted.

SUMMARY

According to aspects of the present invention, systems and methods fortransmission filtering are provided. A receiver includes an inputcoupled to a transmission line to receive distorted optical symbols. Adistortion filter is coupled to the input to replace the distortedoptical symbols with predicted symbols using a trained neural network. Adecoder is coupled to the distortion filter to decode the predictedsymbols.

A method for transmission filtering includes receiving distorted symbolsover a transmission line; identifying the distorted symbols using aneural network, which outputs predicted symbols; and filtering thedistorted symbols by decoding the predicted symbols in place of thedistorted symbols.

Another method for transmission filtering includes inputting symbolsreceived over a transmission system to a neural network as an input;adjusting weights to program the neural network to yield transmittedsymbols transmitted over the transmission system; and mitigating filternarrowing over a transmission line by: identifying distorted symbolsover the transmission line using the neural network, which outputspredicted symbols; and filtering the distorted symbols by decoding thepredicted symbols in place of the distorted symbols.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 is a block/flow diagram illustrating a high-level system/methodfor training a neural network for symbol distortion filtering inaccordance with the present invention;

FIG. 2 is a block/flow diagram illustrating a high-level system/methodfor training the neural network of FIG. 1 in greater detail for symboldistortion filtering in accordance with the present invention;

FIG. 3 is a schematic diagram illustrating a neural network inaccordance with the present invention;

FIG. 4 is a block/flow diagram illustrating a system/method fordistortion filtering transmission symbols in accordance with the presentinvention;

FIG. 5 is a plot of quality factor (dB) versus optical signal to noiseratio (OSNR) (dB) showing one trace with distortionmitigation/compensation in accordance with the present invention andanother trace without distortion mitigation;

FIG. 6 is a block/flow diagram illustrating a system/method for neuralnetwork training and/or distortion filtering in accordance with oneembodiment of the present invention;

FIG. 7 is a flow diagram illustrating methods for distortion filteringtransmission symbols in accordance with one embodiment of the presentinvention; and

FIG. 8 is a flow diagram illustrating methods for distortion filteringtransmission symbols with initial or ongoing training in accordance withanother embodiment of the present invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

In accordance with aspects of the present invention, systems and methodsare provided that employ a neural network-based machine learningapproach to compensate for filter narrowing effects. This approach canonly employ transmission and receiver symbols to train the neuralnetwork, and then uses the neural network to mitigate/compensate for thefilter narrowing. The neural network does not need system information(e.g. baud rate, number of filters, filter bandwidth, optical signal tonoise ratio (OSNR), etc.) and therefore provides systems with achievableperformance improvements with a high degree of independence.

Aspects of the present invention construct a neural network and predictfilter narrowing induced inter-symbol interference (FN-ISI) to optimizethe system performance. The predicted FN-ISI can be employed to adjustthe interpretation of symbols to improve validation of the symbolsduring information (symbol) transmission. The neural network can betrained using known transmissions and can employ the use of differentneural network architectures to achieve a best training performance anda best validation performance. The trained neural network can beemployed to predict the transmission symbols from distorted symbols at areceiver of the transmission system.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable storage medium such as a semiconductor or solid-statememory, magnetic tape, a removable computer diskette, a random-accessmemory (RAM), a read-only memory (ROM), a rigid magnetic disk and anoptical disk, etc.

Each computer program may be tangibly stored in a machine-readablestorage media or device (e.g., program memory or magnetic disk) readableby a general or special purpose programmable computer, for configuringand controlling operation of a computer when the storage media or deviceis read by the computer to perform the procedures described herein. Theinventive system may also be considered to be embodied in acomputer-readable storage medium, configured with a computer program,where the storage medium so configured causes a computer to operate in aspecific and predefined manner to perform the functions describedherein.

A data processing system suitable for storing and/or executing programcode may include at least one processor coupled directly or indirectlyto memory elements through a system bus. The memory elements can includelocal memory employed during actual execution of the program code, bulkstorage, and cache memories which provide temporary storage of at leastsome program code to reduce the number of times code is retrieved frombulk storage during execution. Input/output or I/O devices (includingbut not limited to keyboards, displays, pointing devices, etc.) may becoupled to the system either directly or through intervening I/Ocontrollers.

Network adapters may also be coupled to the system to enable the dataprocessing system to become coupled to other data processing systems orremote printers or storage devices through intervening private or publicnetworks. Modems, cable modem and Ethernet cards are just a few of thecurrently available types of network adapters.

Referring now in detail to the figures in which like numerals representthe same or similar elements and initially to FIG. 1, a high-levelsystem 100 for symbol transmission is illustratively depicted inaccordance with one embodiment of the present invention. The system 100can be employed using any transmission system 102 including wired orwireless systems. However, in one embodiment, transmission system 102includes an optical transmission system. Optical transmission systemscan include fiber optic networks and can be employed in a plurality ofapplications, such as fiber to the home, trans-oceanic transmissionlines, printed wiring board transmissions, etc. The system 100 canemploy single mode fiber(s), multi-mode fiber(s) or any other opticaltransmission media.

It should be understood that the transmission system 102 can includeadditional components, such as splitters, optical to electricalconverters, electrical to optical converters, repeaters, multiplexers,etc. The transmission system 102 can include a single line or caninclude an entire network.

A transmitter 101 can include an encoder 114 for encoding data. Forexample, a pair of data signals (dx and dy) can be encoded using anM-dimensional constellation to generate a set of M drive signals. Anencoding scheme of the encoder 114 in which an N-symbol constellation isdefined in an M-dimensional space can include data words that areencoded as one or more symbols of the constellation. These symbols canthen be modulated by the transmitter onto the available dimensions ofthe optical carrier (102) in one or more signaling intervals of durationT.

The drive signals are then supplied to a modulator 118 for modulatingrespective dimensions of, e.g., a continuous wave (CW) optical carrierin accordance with the drive signals. In the example, a pair of datasignals (e.g., dx and dy) may be encoded as M=4 drive signals, which arethen used to modulate two dimensions (e.g., phase and amplitude, or Iand Q) of each orthogonal polarization of the optical carrier. The CWcarrier may be generated by a laser, and the modulator 118 may beimplemented using, e.g., a phase modulator, variable optical attenuator,Mach-Zehnder interferometers, etc. The modulator 118 generates symbolsfor optical signal transmission. A modulated optical signal 122 at theoutput of the modulator is transmitted through an optical fiber link inthe transmission system 102 to a receiver 103.

The receiver 103 is configured to receive and detect the transmitteddata signals (symbols). The receiver 103 can include a decoder 113. Thedecoder 113 can include a polarization beam splitter for splitting thereceived optical signal into received X and Y polarizations, an opticalhybrid for separately mixing the X and Y polarizations with a localoscillator and a set of photodetectors for detecting the optical powerof each of the mixing products generated by the optical hybrid. AnAnalog to Digital (A/D) converter can be employed to sample eachphotodetector current, and the resulting sample streams, which representone of the modulated dimensions of the optical carrier field, which areprocessed by a Digital Signal Processor (DSP) 120 in accordance with theM-dimensional constellation to generate recovered signals Rx and Ry thatcorrespond with the transmitted data signals dx and dy.

During training, the system 100 includes a neural network model 104 thatreceives the symbols output from the transmitter 101 and from thereceiver 103. Since the received symbols at the receiver 103 have beentransmitted over the transmission system 102, the symbols have undergonedistortion, an in particular intersymbol interference (ISI). ISI is aform of distortion of a signal in which one symbol interferes withsubsequent symbols. This makes previously transmitted symbols have asimilar effect as noise, making the communication less reliable. Thespreading of the pulse beyond its allotted time interval causes it tointerfere with neighboring pulses. ISI is usually caused by multipathpropagation or the inherent linear or non-linear frequency response of acommunication channel causing successive symbols to “blur” together ordistort.

The presence of ISI in the system 100 introduces errors in the decoder113 at the receiver output. This distortion or narrowing effects (e.g.,the effects of ISI) are to be minimized to deliver the digital data toits destination with the smallest error rate possible.

The neural network model 104 is employed in a machine learning approach,which is used for the mitigation of filter narrowing inducedinter-symbol interference (FN-ISI). Based on training symbols, theneural network 104 can predict the function of FN-ISI and thereforecompensate for the FN-ISI for the new receiver symbols. The trainedmodel 104 under a particular system condition (e.g., a particular OSNRvalue) is applicable to compensate for FN-ISI under other systemconditions (e.g., different OSNR levels). Moreover, in a usefulembodiment, the neural network 104 only uses the transmitter symbols andreceiver symbols to train the function of FN-ISI, and therefore does notneed additional system information. No reconfiguration of the signalspectrum or the filter is needed. This improves the spectral efficiencycompared to conventional systems.

The transmitter 101 sends transmission symbols 122 into the transmissionsystem 102, which includes multiple bandwidth-limited filters thatdistort the transmitter symbols 122 resulting in distorted symbols 124.The distorted symbols 124 are received at the receiver 103. In addition,the transmission symbols 122 and the distorted symbols 124 are sent intothe neural network model 104 as a part of training data. The neuralnetwork model 104 then uses the transmission symbols 122 and distortedsymbols 124 as its output and input, respectively, to train a functionof FN-ISI of the transmission system 102. When training is done, thetrained neural network 104 can be used to predict the transmissionsymbols 122 from the distorted symbols 124 to provide predicted symbols105. The predicted symbols 105 can be provided to a decoder or receivedto decode the symbols that have been adjusted or replaced by the neuralnetwork model 104.

The training of the model 104 to handle distorted symbols can betterinterpret the symbols. ISI artifacts can now be readily deciphered andfiltered out using the neural network model 104. Ideally, the predictedsymbols 105 will include the transmission symbols 122.

Referring to FIG. 2, the neural network model 104 for FN-ISI mitigationis described in greater detail. The input of a multi-layer neuralnetwork 104 includes the distorted symbols 201 at the receiver due toFN-ISI of the transmission system 102 at the receiver 103. The output ofthe neural network 202 is the transmission symbols at the transmitter204, respectively. The relationship between the output and input (e.g.,the function of FN-ISI) can be learned by using backpropagation trainingon the training data, trying to minimize the differences betweenpredicted transmission symbols 203 and the actual transmission symbols204.

The neural network model 104 includes a large number of highlyinterconnected processing elements (called “neurons”) working inparallel to solve specific problems. Learning by the neural networkmodel 104 involves adjustments to weights that exist between theneurons. The neural network model 104 is configured for a specificapplication, e.g., learning a function for decoding distorted symbolsthrough the learning process.

Referring to FIG. 3, a neural network is illustratively shown. Theneural network model 104 derives meaning from complicated or imprecisedata and can be used to extract patterns and detect trends that are toocomplex to be detected by humans or other computer-based systems. Thestructure of the neural network model 104 includes input neurons 302that provide information to one or more “hidden” neurons 304.Connections 308 between the input neurons 302 and hidden neurons 304 areweighted, and these weighted inputs are then processed by the hiddenneurons 304 according to some function in the hidden neurons 304, withweighted connections 308 between the layers. There may be any number oflayers of hidden neurons 304, and as well as neurons that performdifferent functions. There exist different neural network structures aswell, such as convolutional neural network, maxout network, etc., whichcan be employed in accordance with the present embodiments.

A set of output neurons 306 accepts and processes weighted input fromthe last set of hidden neurons 304. This represents a “feed-forward”computation, where information propagates from input neurons 302 to theoutput neurons 306. Upon completion of a feed-forward computation, theoutput is compared to a desired output available from training data. Theerror relative to the training data is then processed in “feed-back”computation, where the hidden neurons 304 and input neurons 302 receiveinformation regarding the error propagating backward from the outputneurons 306. Once the backward error propagation has been completed,weight updates are performed, with the weighted connections 308 beingupdated to account for the received error. The error formulationsonce-trained provide the decoding formula for the transmission system102.

It should be understood that any number of these stages may beimplemented, by interposing additional layers of arrays and hiddenneurons 304. It should also be noted that some neurons may be constantneurons, which provide a constant voltage to the array. The constantneurons can be present among the input neurons 302 and/or hidden neurons304 and are only used during feed-forward operation.

During back propagation, the output neurons 306 provide a voltage (orother characteristic) back across the weighted connections 308. Anoutput layer compares the generated network response to training dataand computes an error. The error is applied to the array as a voltagepulse, where the height and/or duration of the pulse is modulatedproportional to the error value. In this example, the back-propagationtravels through the entire neural network 104 until all hidden neurons304 and the input neurons 302 have stored an error value.

During weight update mode, after both forward and backward passes arecompleted, each weight is updated proportional to the product of thesignal passed through the weight during the forward and backward passes.Update signal generators provide pulses in both directions (though notethat, for input and output neurons, only one direction will beavailable). The shapes and amplitudes of the pulses from updategenerators are configured to change a state of the weights, such thatthe resistance of the weights is updated.

It should be noted that the three modes of operation, feed forward, backpropagation, and weight update, do not overlap with one another.However, because the different phases do not overlap, there willnecessarily be some form of control mechanism within in the neurons tocontrol which components are active. It should therefore be understoodthat there may be switches and other structures that are not shown inthe neurons to handle switching between modes.

The weights may be implemented in software or in hardware, for exampleusing relatively complicated weighting circuitry or using resistiveadjustable devices (e.g., resistive processing unit (RPU)).

Referring to FIG. 4, a system 400 includes a receiver 403 having adistortion filter 402. The distortion filter 402 includes the trainedmodel 104 and is employed for predicting the transmission symbols fornew distorted symbols at the receiver 403 to mitigate FN-ISI. The neuralnetwork (NN) model 104 for FN-ISI mitigation improves system performanceby outputting predicted symbols making it easier and more accurate todecode the symbols by the decoder 113. This approach only needs historictransmission symbols and receiver symbols to train the neural network104. Then, the trained neural network 104 can be employed to compensatefor FN-ISI.

This approach does not need additional low-level information such asbaud rate, number of filters, filter bandwidth, OSNR, etc. The trainedneural network 104 has learned the function of the FN-ISI and canpredict the transmission symbols from distorted symbols at the receiver103. However, in one optional embodiment, the receiver 103 can include afeedback sensor which can react to error codes or other feedbackcriteria (e.g., Q-factor) to determine if further training of the NNmodel 104 is needed. For example, if the error rate increases above athreshold, additional training may be needed. The training can beperformed in a training mode 406 activated in accordance with thefeedback sensor 404. It should be understood that the feedback sensor404 may be located between any of the component or software modules andcan employ any useful metric to measure performance.

In another embodiment, the neural network model 104 can be replaced witha function or algorithm gleaned from the neural network training. Inthis embodiment, little memory or processing capability is needed. Inone embodiment, a lookup table or table may be employed to providepredicted symbols based on distorted symbols.

Referring to FIG. 5, an exemplary processing system 500 to which thepresent invention may be applied is shown in accordance with oneembodiment. The processing system 500 can be employed for training aneural network in or in conjunction with a distortion filter 524. Theneural network can be implemented in hardware (e.g., an RPU device) orsoftware. The processing system 500 can also be employed as or with areceiver device (403, FIG. 4). The processing system 500 includes atleast one processor (CPU) 502 operatively coupled to other componentsvia a system bus 505. A cache 506, a Read Only Memory (ROM) 508, aRandom-Access Memory (RAM) 510, an input/output (I/O) adapter 520, asound adapter 530, a network adapter 540, a user interface adapter 550,and a display adapter 560, are operatively coupled to the system bus505.

A first storage device 522 and the distortion filter 524, which can bestored in memory, are operatively coupled to system bus 505 by the I/Oadapter 520. The storage devices 522 and 524 can be any of a diskstorage device (e.g., a magnetic or optical disk storage device), asolid state magnetic device, and so forth. The storage devices 522 and524 can be the same type of storage device or different types of storagedevices.

An optional speaker 532 is operatively coupled to system bus 505 by thesound adapter 530. A receiver 542 is operatively coupled to system bus505 by network adapter 540. In some embodiments, a transceiver ortransmitter may also be employed and connected to the system bus 505through a network adapter. A display device 562 can optionally beincluded and operatively coupled to system bus 505 by display adapter560.

A first user input device 552, a second user input device 554, and athird user input device 556 are operatively coupled to system bus 505 byuser interface adapter 550. The user input devices 552, 554, and 556 canbe any of a keyboard, a mouse, a keypad, an image capture device, amotion sensing device, a microphone, a device incorporating thefunctionality of at least two of the preceding devices, and so forth. Ofcourse, other types of input devices can also be used, while maintainingthe spirit of the present invention. The user input devices 552, 554,and 556 can be the same type of user input device or different types ofuser input devices. The user input devices 552, 554, and 556 are used toinput and output information to and from system 500.

Of course, the processing system 500 may also include other elements(not shown), as readily contemplated by one of skill in the art, as wellas omit certain elements. For example, various other input devicesand/or output devices can be included in processing system 500,depending upon the particular implementation of the same, as readilyunderstood by one of ordinary skill in the art. For example, varioustypes of optical, wireless and/or wired input and/or output devices canbe used. Moreover, additional processors, controllers, memories, and soforth, in various configurations can also be utilized as readilyappreciated by one of ordinary skill in the art. These and othervariations of the processing system 500 are readily contemplated by oneof ordinary skill in the art given the teachings of the presentinvention provided herein.

Referring to FIG. 6, quality factor (Q-factor) in dB is measured andplotted against OSNR (in dB) for a same transmission system. One trace502 shows the transmission system with mitigation/compensation employingthe distortion filter in accordance with the present embodiments.Another trace 504 shows the transmission system without mitigation. Overthe same OSNR range the distortion filter provides a Q-factor of atleast ⅓ dB or greater and the benefits increase with greater OSNR. Inone embodiment, Q-factor can be employed as a feedback measurement todetermine whether further training of the NN model is needed.

Referring to FIG. 7, methods for transmission filtering areillustratively shown. In block 702, distorted symbols are received overa transmission line. The transmission line can include an opticaltransmission line or system, although wired or wireless systems can alsobe employed.

In block 704, the distorted symbols are identified using a neuralnetwork, which outputs predicted symbols. In useful embodiments, theneural network is trained independently of system information using onlytransmitted and received symbols. This makes the model independent ofother system information, e.g., baud rate, number of filters, filterbandwidth, OSNR and/or other system information.

In block 706, the distorted symbols are filtered by decoding thepredicted symbols in place of the distorted symbols. The distortedsymbols filtering compensates for filter narrowing effects of thetransmission line or system. The distorted symbols can bereplaced/filtered to predict filter narrowing induced inter-symbolinterference (FN-ISI).

In block 708, performance of the predicted symbols can be measured usinga feedback sensor. The performance measurement can include measuring anerror rate, Q-factor, line or channel degradations, etc.

In block 710, a training mode can be triggered by the feedback sensor ifperformance of the predicted symbols drops below a threshold. Thethreshold can be user set, set by default or set automatically.

Referring to FIG. 8, methods for transmission filtering including neuralnetwork training are illustratively shown. In block 802, symbolsreceived over a transmission system are input to a neural network as aninput. In block 804, the neural network is programmed by adjustingweights (in a weight array) of the network to yield transmitted symbolstransmitted over the transmission system. In block 806, filter narrowingdue to a transmission line or system (e.g., FN-ISI) is mitigated. Inblock 808, distorted symbols received over the transmission line areidentified using the neural network, which outputs predicted symbols. Inblock 810, the distorted symbols are filtered by predicting thetransmitted symbols and substituting the predicted symbols in place ofthe distorted symbols.

In block 812, the neural network is trained independently of systeminformation, where system information includes one or more of: baudrate, number of filters, filter bandwidth, OSNR, etc.

In block 814, performance of the predicted symbols can be measured usinga feedback sensor. The performance measurement can include measuring anerror rate, Q-factor, line or channel degradations, etc.

In block 816, a training mode can be triggered by the feedback sensor ifperformance of the predicted symbols drops below a threshold. Thethreshold can be user set, set by default or set automatically.

The foregoing is to be understood as being in every respect illustrativeand exemplary, but not restrictive, and the scope of the inventiondisclosed herein is not to be determined from the Detailed Description,but rather from the claims as interpreted according to the full breadthpermitted by the patent laws. It is to be understood that theembodiments shown and described herein are only illustrative of thepresent invention and that those skilled in the art may implementvarious modifications without departing from the scope and spirit of theinvention. Those skilled in the art could implement various otherfeature combinations without departing from the scope and spirit of theinvention. Having thus described aspects of the invention, with thedetails and particularity required by the patent laws, what is claimedand desired protected by Letters Patent is set forth in the appendedclaims.

What is claimed is:
 1. A receiver, comprising: an input coupled to atransmission line to receive distorted optical symbols; a distortionfilter coupled to the input to replace the distorted optical symbolswith predicted symbols using a trained neural network; and a decodercoupled to the distortion filter to decode the predicted symbols.
 2. Thereceiver as recited in claim 1, wherein the distortion filtercompensates for filter narrowing effects.
 3. The receiver as recited inclaim 1, wherein the distortion filter predicts filter narrowing inducedinter-symbol interference (FN-ISI).
 4. The receiver as recited in claim1, wherein the trained neural network is trained independently of systeminformation, where system information includes one or more of: baudrate, number of filters, filter bandwidth, and/or optical signal tonoise ratio (OSNR).
 5. The receiver as recited in claim 1, furthercomprising a feedback sensor to measure performance of the predictedsymbols.
 6. The receiver as recited in claim 5, further comprising atraining mode triggered by the feedback sensor if performance of thepredicted symbols drops below a threshold.
 7. A method for transmissionfiltering, comprising: receiving distorted symbols over a transmissionline; identifying the distorted symbols using a neural network, whichoutputs predicted symbols; and filtering the distorted symbols bydecoding the predicted symbols in place of the distorted symbols.
 8. Themethod as recited in claim 7, wherein filtering the distorted symbolscompensates for filter narrowing effects.
 9. The method as recited inclaim 7, wherein filtering the distorted symbols predicts filternarrowing induced inter-symbol interference (FN-ISI).
 10. The method asrecited in claim 7, wherein the transmission line includes an opticaltransmission line.
 11. The method as recited in claim 7, wherein theneural network is trained independently of system information, wheresystem information includes one or more of: baud rate, number offilters, filter bandwidth, and/or optical signal to noise ratio (OSNR).12. The method as recited in claim 7, further comprising measuringperformance of the predicted symbols using a feedback sensor.
 13. Themethod as recited in claim 12, wherein measuring performance includesmeasuring an error rate.
 14. The method as recited in claim 12, whereinmeasuring performance includes measuring a quality factor.
 15. Themethod as recited in claim 12, further comprising triggering a trainingmode by the feedback sensor if performance of the predicted symbolsdrops below a threshold.
 16. A method for transmission filtering,comprising: inputting symbols received over a transmission system to aneural network as an input; adjusting weights to program the neuralnetwork to yield transmitted symbols transmitted over the transmissionsystem; and mitigating filter narrowing over a transmission line by:identifying distorted symbols over the transmission line using theneural network, which outputs predicted symbols; and filtering thedistorted symbols by decoding the predicted symbols in place of thedistorted symbols.
 17. The method as recited in claim 16, whereinfiltering narrowing includes filter narrowing induced inter-symbolinterference (FN-ISI).
 18. The method as recited in claim 16, whereinthe neural network is trained independently of system information, wheresystem information includes one or more of: baud rate, number offilters, filter bandwidth, and/or optical signal to noise ratio (OSNR).19. The method as recited in claim 16, further comprising measuringperformance of the predicted symbols using a feedback sensor.
 20. Themethod as recited in claim 19, further comprising triggering a trainingmode by the feedback sensor if performance of the predicted symbolsdrops below a threshold.